An Empirical Study of Robust Portfolios Based on Statistical Noise Reduction and Regularization Constraints

Abstract

This research paper discusses the issue of out-of-sample robustness of portfolio optimization within a complex market environment. Within the mean-variance framework, we compare four methods for covariance estimation and weighting: a baseline model based on sample covariances, the Ledoit-Wolf shrinkage estimator, Garber's robust covariance estimator, and a minimum-variance model incorporating an L2 regularization term. This study uses data from 60 American stocks from 2019 to 2021, with four rebalancing cycles (5, 20, 60, and 100 days) were established, and a moving-window backtesting method was applied to evaluate the performance of the various methods in terms of returns, risk, and out-of-sample stability. The empirical results indicate that the L2 normalization model generates higher cumulative returns and Sharpe ratios during most rebalancing periods, demonstrating effective stabilization of the weights; Garbner's robust covariance technique demonstrates consistent resilience to downturns in high-volatility market environments; And Reduit-Wolf's contraction estimates also show a relatively stable improvement in sample skewness compared to the benchmark model. These results suggest that including a covariance noise or normalization term in the traditional expected value and variance-based approach to portfolio management helps reduce the impact of estimation error and market volatility on portfolio performance. The period of analysis for this paper is specified. Furthermore, it covers the observation period, highlights limitations related to market comprehensiveness and parameter selection, and provides guidance for future research by incorporating financial data from diverse sources and more advanced robust optimization techniques.